Question

Exercise 1: In the refraction of light, Snell's law relates the angle of incidence θǐne to the angle of refraction Orefr by the formula ninc sin θ¡nc-nrefr sin θrefr where nin and nidi are the refractive index of the incident and refracted medium, respectively. Derive a formula for the change in refracted angle AGhefr due to a small change in the refractive index Δnrefr. Exercise 2: The acceleration due to gravity g can be obtained by measuring the period T of a pendulum of length L and the formula g = (2n)2L What is acceleration due to gravity if L 1.20 0.01) m and T- (2.20 0.01) s?

Answer 1

N_inc sin theta_inc = n_refr sin theta_refr 0 = delta n_refer sin theta_refr + n_refr cos theta_refr delta theta_refr delta theta_refr = -delta n_refr sin theta_refr /cos theta_refr delta theta_refr = -delta n_refr tan theta_refr L = (1.20 plusminus 0.01) m T = (2.20 plusminus 0.01) s g = 4 pi^2 L/T^2 = 4 times pi^2 times 1.20/(2.20)^2 g = 9.78 m/s^2 delta g/g = delta L/L + 2 delta T/T delta g/g = (0.01/1.2 + 2 times 0.01/2.2) = 0.0174 delta g = g times 0.0174 = 0.17 g = (9.78 plusminus 0.17) m/s^2